Related papers: Improved Landau Gauge Fixing and Discretisation Er…
An important and difficult problem in optimization is the high-order unconstrained binary optimization, which can represent many optimization problems more efficient than quadratic unconstrained binary optimization, but how to quickly solve…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
In this paper we discuss the use of implicit Runge-Kutta schemes for the time discretization of optimal control problems with evolution equations. The specialty of the considered discretizations is that the discretizations schemes for the…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
We show that QCD Green functions in Landau Gauge exhibit sizable $O(1/\mu^2)$ corrections to the expected perturbative behavior at energies as high as 10 GeV. We argue that these are due to a $<A^2>$-condensate which does not vanish in…
We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee…
The Gribov ambiguity problem is studied for compact lattice QED within the Lorentz gauge. In the Coulomb phase, Gribov copies are mainly caused by double Dirac sheets and zero-momentum modes of the gauge fields. Removing them by (non-)…
A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…
When fixing a covariant gauge, most popularly the Landau gauge, on the lattice one encounters the Neuberger 0/0 problem which prevents one from formulating a Becchi--Rouet--Stora--Tyutin symmetry on the lattice. Following the interpretation…
We consider recent progress in algorithms for generating gauge field configurations that include the dynamical effects of light fermions. We survey what has been achieved in recent state-of-the-art computations, and examine the trade-offs…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
The implementation of the linear covariant gauge on the lattice faces a conceptual problem: using the standard compact discretization, the gluon field is bounded, while the four-divergence of the gluon field satisfies a Gaussian…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
In this paper, we propose two linearized finite difference schemes for solving the logarithmic Schr\"odinger equation (LogSE) without the need for regularization of the logarithmic term. These two schemes employ the first-order and the…
In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable…
Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly…
In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional,…
In this more technical part we give additional details on the gauge-fixing approach presented in hep-lat/9709113. We also explain how the gauge-fixing approach evades the Nielsen-Ninomiya no-go theorem.
The infrared behaviour of QCD Green's functions in Landau gauge has been focus of intense study. Different non-perturbative approaches lead to a prediction in line with the conditions for confinement in local quantum field theory as spelled…